Related papers: On spectral representations of tensor random field…
We study a compound Poisson random field on plane and examine its various fractional variants. We derive the distributions of these random fields and in some particular cases, obtain their associated system of governing differential…
Primordial scalar perturbations may be generated when complex conformal scalar field rolls down its negative quartic potential. We begin with the discussion of peculiar infrared properties of this scenario. We then consider the statistical…
This work provides a computationally efficient and statistically consistent moment-based estimator for mixtures of spherical Gaussians. Under the condition that component means are in general position, a simple spectral decomposition…
We prove a general representation stability result for polynomial coefficient systems which lets us prove representation stability and secondary homological stability for many families of groups with polynomial coefficients. This gives two…
The tensor flattenings appear naturally in quantum information when one produces a density matrix by partially tracing the degrees of freedom of a pure quantum state. In this paper, we study the joint $^*$-distribution of the flattenings of…
In this note, we provide a important considerations of a familiar topic: the gradient of a vector field. The gradient of a vector field is a common quantity represented in continuum mechanics. However, even for Cartesian coordinate systems,…
In this paper, we study modulus of continuity and rate of convergence of series of conditionally sub-Gaussian random fields. This framework includes both classical series representations of Gaussian fields and LePage series representations…
In the state-vector space for relativistic quantum fields a new set of basis vectors are introduced, which are taken to be eigenstates of the field operators themselves. The corresponding eigenvalues are then interpreted as representing…
We present novel equivalences in random matrix and tensor models between complex and self-adjoint theories with nontrivial quadratic terms in the action, established through an intermediate field representation. More precisely, we show that…
The representation theory of tensor functions is a powerful mathematical tool for constitutive modeling of anisotropic materials. A major limitation of the traditional theory is that many point groups require fourth- or sixth-order…
We formulate a generalized scattering field theory a la Buttiker describing particles transport in magnetic/superconducting heterostructures. The proposed formalism, characterized by a four- component spinorial wavefunction of the…
Using the decomposition of semimagic squares into the associated and balanced symmetry types as a motivation, we introduce an equivalent representation in terms of block-structured matrices. This block representation provides a way of…
Motion of test particles in the gravitational field associated with an electromagnetic plane wave is investigated. The interaction with the radiation field is modeled by a force term {\it \`a la} Poynting-Robertson entering the equations of…
A continuum model to study the influence of dislocations on the electronic properties of condensed matter systems is described and analyzed. The model is based on a geometrical formalism that associates a density of dislocations with the…
The power and the probability of electromagnetic radiation from an electron in a constant background tensor field violating Lorentz invariance are calculated. The case of a background field of the quasielectric type is considered. The…
Abstract. The purpose of this paper is twofold. We introduce the theory of random tensors, which naturally extends the method of random averaging operators in our earlier work arXiv:1910.08492, to study the propagation of randomness under…
Motivated by the subordinated Brownian motion, we define a new class of (in general discontinuous) random fields on higher-dimensional parameter domains: the subordinated Gaussian random field. We investigate the pointwise marginal…
Spatial symmetries of the densities appearing in the nuclear Density Functional Theory are discussed. General forms of the local densities are derived by using methods of construction of isotropic tensor fields. The spherical and axial…
The signature of a path is a sequence of tensors whose entries are iterated integrals, playing a key role in stochastic analysis and applications. The set of all signature tensors at a particular level gives rise to the universal signature…
A sketch is given of a circle of ideas relating quantum field theories with representation theory. The main mathematical ingredients are spinor geometry and the gauge group equivariant K-theory of the space of connections.